This study introduces numerical advancements in an alternative design for the SPS Beam Dump Facility (BDF) at CERN. The design envisions a high-power operation target made of flowing liquid lead. The BDF is a proposed versatile facility at CERN, intended for both beam-dump-like and fixed-target experiments. The target behavior is assessed, assuming a proton beam with a momentum of 400 GeV/c, a pulse frequency of 1/7.2 Hz, and an average beam power of 355 kW. An evaluation is conducted using various Computational Fluid Dynamics (CFD) codes to analyze the behavior of liquid lead and to predict the thermal stress on the target vessel induced by the pulsed heat source generated by the charged particle beam. The comparison increases the reliability of the results, investigating the dependencies on the CFD modeling approach. The beam is modeled as a volumetric heat source with data coming from beam-lead interaction simulations provided by CERN and obtained with the Monte-Carlo code FLUKA. The velocity field and stress profiles are utilized to enhance the design of the lead loop and verify its viability and safety when operated with a liquid metal target.